1. Field of the Disclosure
The disclosure relates generally to the field of seismic data processing. In particular, methods of the disclosure relate to the extraction of common image gathers (CIGs) in the angle domain.
2. Description of the Related Art
Seismic surveying may be used to determine structures, compositions and fluid content of subsurface Earth formations. For instance, seismic surveying may be used to infer the presence of useful materials, such as oil and gas, in subsurface Earth formations. In seismic exploration for oil and gas, the Earth's subsurface may be illuminated by a seismic source at or near the surface of the Earth. As used herein, the term “illumination” means at least that seismic energy from the source is incident on a subsurface point. Scattered or reflected energy from the illuminated subsurface point may be recorded by one or more sensors or receivers deployed for detecting seismic energy originating from the source. Impedance boundaries are frequently located at boundaries between Earth formations having different composition. Waves propagate into the Earth and may be reflected from the impedance boundaries and travel upwardly until being detected by seismic sensors. Structure and composition of the Earth's subsurface may be inferred from the travel time of the reflected seismic energy, from the geographic position of the source and each of the sensors, and from the amplitude and phase of the various frequency components of the reflected seismic energy. Reflected waves are typically recorded by a receiver array. The receivers can be positioned on the Earth's surface, on the ocean bottom, towed near a water surface, or in a well and can be arranged in any geometrical pattern in two or three dimensions. In a seismic survey, the source and receiver array are often relocated to a number of overlapping areas in order to uniformly illuminate the subsurface in a region.
FIG. 1 illustrates diagrammatically an example of a survey of seismic data with a source S of seismic waves and an array of receivers G. It also shows a point C of the subsurface which is assumed to contribute to the signal sensed by one of the receivers G. The horizontal coordinates of point C of the subsurface are denoted by x, y (or only one spatial coordinate if 2D imaging instead of 3D imaging is considered), while its depth is denoted by z. FIG. 1 also provides a simplified representation (dashed lines) of the propagation of seismic waves from the source S to the point C and from the point C to the receiver G. The waves may be refracted at discontinuities of the geological layers where the impedance changes and reflected or diffracted at different positions including that of point C.
The data recorded in a seismic survey include, for each shot from a source S and for each receiver G, a seismic trace which is a time series of the signal sensed by the receiver G. The traces for a number of shots must be transformed to provide an image of the subsurface which will be the result of stacking or integrating a large amount of information. An important step of the transformation is the migration which consists in processing the data with respect to a model such that the data received at the surface are mapped into subsurface to represent the reflectivity of the discontinuities in the model. The model is usually a map of the propagation velocity of the acoustic waves in the subsurface. This model is not known a priori and it is a main challenge of many seismic imaging technologies to determine a model that will properly account for the field data.
In pre-stack depth migration (PSDM) methods, migrated data are computed for each shot using the velocity model and arranged in an output cube containing migrated values associated with positions in the subsurface. The cubes obtained for different shots may then be stacked and/or analyzed to form Common Image Gathers (CIGs) and check consistency of the model. The model may be corrected and the process iterated until a satisfactory image is obtained.
CIGs are popular tools for evaluating the migration velocity field, for subsurface attribute analysis, and for imaging enhancement. CIGs are created either during the migration process or from data extracted from the output cubes of migration, sorted in a convenient way for analysis so as to check the velocity model. A CIG is a bi-dimensional data structure defined for a given horizontal position (x, y), with a first axis representing the depth z and a second axis representing a domain parameter a referred to for sorting the multiple images of the migration process. It contains reflectivity values obtained from the output cubes resulting from the migration, forming an image which can be analyzed to check and/or correct the velocity model. Examples of commonly used domain parameters a include the surface offset, subsurface offset or the scattering or reflection angle at the subsurface position (x, y, z), etc. Because CIGs in the scattering angle domain closely represent the angle-dependent reflectivity of subsurface reflectors, they are the most useful for velocity model analysis, subsurface attribute analysis and image improvement in complex media.
The computation of CIGs is not simple in all wave-field extrapolation methods and it can be very expensive for reverse-time migration (RTM), which by itself is already a process requiring a large amount of computation time and computer memory. RTM is a two-way migration solution which can accurately describe wave propagation in complex media. It is increasingly used in seismic exploration by virtue of advances in computer power and programming.
In “Offset and angle-domain common image-point gathers for shot-profile migration”, Geophysics, Vol. 67, No. 3, 2002, pp. 883-889, J. Rickett and P. Sava established the notion of subsurface offset CIGs which requires the extension of the imaging condition through the computation of the correlation function along the spatial horizontal dimension. This type of gather is the most common way to output wave-equation-based migration images. It corresponds to velocity updating techniques based on focusing analysis, which look for the highest correlation at zero-time lag and/or zero-offset, and only small values elsewhere. A method has been proposed to derive scattering angle CIGs from subsurface offset CIGs by applying local slant stack. A similar method has also been proposed to extend the imaging condition in the time domain and to convert the time-shifted image gathers to CIGs into the angle domain.
The local offset and time lag gathers are formed during the migration process, and significant computer memory is required to store the intermediate CIGs. For 3-D cases, a 5-D array is necessary where local offsets in both x and y directions are used; if all space and time lags are included, a 7-D array is necessary. While applying an imaging condition may normally require only a small proportion of the memory needed in the whole computation of RTM, the memory requirements may increase dramatically if a large number of lags are computed in more than one dimension. Another major part of the computation cost is the use of slant stacking to extract angle gathers from local offset (or time lag) gathers. While local slant stack may be an efficient procedure in 2-D, the gather conversion is very complex in 3-D. While potentially less expensive to derive angle gathers from CIGs with only non-zero time lag the resolution of angle gathers from this approach is not as good as those provided by local offset gathers. Furthermore, this methodology does not provide azimuth information for 3-D cases.
In another example, angle domain CIGs can be formed during the migration process by wave field decomposition. Source and receiver wave fields in the frequency domain are transformed into the wave-number domain, cross-correlation is applied between each component of the source wave field and that of the receiver wave field, and then the resulting partial images are mapped and binned according to the corresponding azimuth and reflection angle to form angle-domain CIGs. Wave field decomposition can be performed in the time and space domain by local slant stack as well. A 4-D spatial/temporal Fourier transform is applied to both the source and receiver wave fields to convert them into frequency wave-number domain. The procedure to generate angle dependent partial images typically involves an expensive multi-dimensional convolution of seven loops. A 3-D inverse spatial Fourier transform is applied to the angle dependent image formed initially in the wave-number domain. Spatial windowing, ALFT (anti-aliasing Fourier transform) and the facts that the norm of slowness in a small window in a homogeneous media varies only in a small range and the seismic events are closer to linear help to reduce the cost to make the approach feasible in practice. The cost of this migration has been estimated to be 5-10 times the cost of the RTM itself. Besides intensive computation, this method requires significant disk space to store the wave fields at all time steps and significant memory to store the 5-D angle gathers.
In still another example, instead of wave-field decomposition, the direction of wave propagation is computed at each time step, partial images are computed together with the corresponding angles, and then mapped accordingly into angle gathers. This approach determines the dominant direction of wave propagation during the migration process. The additional computation cost is caused by computing the Poynting vectors of the wave fields, which is similar to that of a RTM. However when the wave field is complex it is difficult to detect the direction of wave propagation accurately.